Elasticity Solutions for Thick-Wall Submersible Spheres

Elasticity solutions utilizing the classical Boussinesq potential functions for thick-wall submersible spheres are developed. The solutions provide field stresses and strains, which consider the effect of gravity body forces, and arbitrary boundary loadings. The boundary loadings may be due to a nonuniform hydrostatic pressure, hull equipment, ballast, and can be expressed as an infinite series of Legendre polynomials. A numerical example which considers a nonuniform hydrostatic pressure and an arbitrary counter-buoyancy force applied at the inner boundary is given. Field stresses and strains are presented for various shell thicknesses and hydrostatic pressures.